Proposition 1, p. 11 — cross-licensing weakly raises supplier profit ex post

Fix innovation levels $0\le T_1\le T_2$, effectiveness $0\le\beta\le1$, and a wholesale price $r\ge0$. The manufacturers' quantity game has a Nash equilibrium both with cross-licensing at effectiveness $\beta$ and without it at $\beta=0$. For every equilibrium $q^{\mathrm{cl}}$ of the former game and every equilibrium $q^{\mathrm n}$ of the latter,

This is the supplier's ex-post profit comparison at the same innovation levels and the same wholesale price. Formalization Note The weak inequality permits equality, in particular at $\beta=0$. The paper's second sentence interprets this comparison as the final contract choice; it does not specify a separate contract-stage game. Nonnegative $r$ is made explicit because the claim fails at a negative wholesale price.